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A112179 McKay-Thompson series of class 40B for the Monster group. 2
1, 2, 1, 2, 4, 6, 9, 8, 13, 20, 22, 28, 34, 46, 57, 68, 87, 104, 127, 152, 187, 232, 267, 318, 388, 462, 545, 632, 753, 896, 1043, 1216, 1416, 1664, 1928, 2228, 2597, 2996, 3454, 3976, 4585, 5286, 6031, 6900, 7918, 9060, 10325, 11720, 13372, 15228 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(sqrt(2*n/5)*Pi) / (2^(5/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

Expansion of q^(1/2)*((eta(q^2)*eta(q^10))^2/(eta(q)*eta(q^4)*eta(q^5) *eta(q^20)))^2 in powers of q. - G. C. Greubel, Feb 13 2018

EXAMPLE

T40B = 1/q +2*q +q^3 +2*q^5 +4*q^7 +6*q^9 +9*q^11 +8*q^13 +...

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[((1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *)

eta[q_] := q^(1/24)*QPochhammer[q]; e40B:= q^(1/2)*((eta[q^2]*eta[q^10] )^2/(eta[q]*eta[q^4]*eta[q^5]*eta[q^20]))^2; Table[ SeriesCoefficient[ e40B, {q, 0, n}], {n, 0, 50}] (* G. C. Greubel, Feb 13 2018 *)

PROG

(PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^10))^2/(eta(q)*eta(q^4)* eta(q^5)*eta(q^20)))^2; Vec(A) \\ G. C. Greubel, Jun 16 2018

CROSSREFS

Sequence in context: A283334 A301413 A305056 * A058553 A038067 A136102

Adjacent sequences:  A112176 A112177 A112178 * A112180 A112181 A112182

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified October 21 02:22 EDT 2018. Contains 316405 sequences. (Running on oeis4.)